Prime numbers between 6401 and 6,500
There are 8 prime numbers between 6401 and 6,500: 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491.
How to work it out
- 1
A prime has exactly two factors, 1 and itself. To list them, cross out multiples of 2, then 3, then 5, and so on up to ā6500 ā 80.6 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 8 primes between 6401 and 6,500, with a total of 51,662.
- 3
The biggest gap between neighbouring primes in this range is 22, after 6427 (the next prime is 6449). There are 1 twin prime pairs (primes 2 apart): (6449, 6451).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 6,401 to 6,410 | 0 | 0% |
| 6,411 to 6,420 | 0 | 0% |
| 6,421 to 6,430 | 2 | 20% |
| 6,431 to 6,440 | 0 | 0% |
| 6,441 to 6,450 | 1 | 10% |
| 6,451 to 6,460 | 1 | 10% |
| 6,461 to 6,470 | 1 | 10% |
| 6,471 to 6,480 | 1 | 10% |
| 6,481 to 6,490 | 1 | 10% |
| 6,491 to 6,500 | 1 | 10% |
Questions
How many prime numbers are there between 6401 and 6,500?
8.
What is the biggest prime number below 6,500?
6491.
What is the first prime number after 6400?
6421.